Valid Inequality

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Yang Zhenglin - One of the best experts on this subject based on the ideXlab platform.

  • Valid Inequality analysis on polytope of unit status in unit commitment
    2011
    Co-Authors: Xu Fan, Yao Jianguo, Geng Jian, Yang Zhenglin
    Abstract:

    The "loose and tight" extent of Valid inequalities of minimum start-up and trip-out time constraints in the mixed integer programming model for unit commitment problem directly impacts the performance of the algorithm to solve the model. Firstly, the authors give an intuitive criterion to judge the superior and inferior of Valid inequalities in the viewpoint of geometry, i.e., the scale of the slack problem's feasible domain; then various Valid inequalities of commonly used minimum start-up and trip-out time constraints are analyzed, thus the Valid Inequality of minimum start-up and trip-out time of one unit, which is theoretically most "tight", is obtained; finally, the correctness of the most "tight" Valid Inequality is verified by simulation results of IEEE RTS 96 system and calculation of actual example.

Xu Fan - One of the best experts on this subject based on the ideXlab platform.

  • Valid Inequality analysis on polytope of unit status in unit commitment
    2011
    Co-Authors: Xu Fan, Yao Jianguo, Geng Jian, Yang Zhenglin
    Abstract:

    The "loose and tight" extent of Valid inequalities of minimum start-up and trip-out time constraints in the mixed integer programming model for unit commitment problem directly impacts the performance of the algorithm to solve the model. Firstly, the authors give an intuitive criterion to judge the superior and inferior of Valid inequalities in the viewpoint of geometry, i.e., the scale of the slack problem's feasible domain; then various Valid inequalities of commonly used minimum start-up and trip-out time constraints are analyzed, thus the Valid Inequality of minimum start-up and trip-out time of one unit, which is theoretically most "tight", is obtained; finally, the correctness of the most "tight" Valid Inequality is verified by simulation results of IEEE RTS 96 system and calculation of actual example.

Wook Kim - One of the best experts on this subject based on the ideXlab platform.

  • fault current constraint transmission expansion planning based on the inverse matrix modification lemma and a Valid Inequality
    2019
    Co-Authors: Sungwoo Lee, Hyoungtae Kim, Tae Hyun Kim, Hansol Shin, Wook Kim
    Abstract:

    In the transmission expansion planning (TEP) problem, it is challenging to consider a fault current level constraint due to the time-consuming update process of the bus impedance matrix, which is required to calculate the fault currents during the search for the optimal solution. In the existing studies, either a nonlinear update equation or its linearized version is used to calculate the updated bus impedance matrix. In the former case, there is a problem in that the mathematical formulation is derived in the form of mixed-integer nonlinear programming. In the latter case, there is a problem in that an error due to the linearization may exist and the change of fault currents in other buses that are not connected to the new transmission lines cannot be detected. In this paper, we use a method to obtain the exact updated bus impedance matrix directly from the inversion of the bus admittance matrix. We propose a novel method based on the inverse matrix modification lemma (IMML) and a Valid Inequality is proposed to find a better solution to the TEP problem with fault current level constraint. The proposed method is applied to the IEEE two-area reliability test system with 96 buses to verify the performance and effectiveness of the proposed method and we compare the results with the existing methods. Simulation results show that the existing TEP method based on impedance matrix modification method violates the fault current level constraint in some buses, while the proposed method satisfies the constraint in all buses in a reasonable computation time.

Yao Jianguo - One of the best experts on this subject based on the ideXlab platform.

  • Valid Inequality analysis on polytope of unit status in unit commitment
    2011
    Co-Authors: Xu Fan, Yao Jianguo, Geng Jian, Yang Zhenglin
    Abstract:

    The "loose and tight" extent of Valid inequalities of minimum start-up and trip-out time constraints in the mixed integer programming model for unit commitment problem directly impacts the performance of the algorithm to solve the model. Firstly, the authors give an intuitive criterion to judge the superior and inferior of Valid inequalities in the viewpoint of geometry, i.e., the scale of the slack problem's feasible domain; then various Valid inequalities of commonly used minimum start-up and trip-out time constraints are analyzed, thus the Valid Inequality of minimum start-up and trip-out time of one unit, which is theoretically most "tight", is obtained; finally, the correctness of the most "tight" Valid Inequality is verified by simulation results of IEEE RTS 96 system and calculation of actual example.

Geng Jian - One of the best experts on this subject based on the ideXlab platform.

  • Valid Inequality analysis on polytope of unit status in unit commitment
    2011
    Co-Authors: Xu Fan, Yao Jianguo, Geng Jian, Yang Zhenglin
    Abstract:

    The "loose and tight" extent of Valid inequalities of minimum start-up and trip-out time constraints in the mixed integer programming model for unit commitment problem directly impacts the performance of the algorithm to solve the model. Firstly, the authors give an intuitive criterion to judge the superior and inferior of Valid inequalities in the viewpoint of geometry, i.e., the scale of the slack problem's feasible domain; then various Valid inequalities of commonly used minimum start-up and trip-out time constraints are analyzed, thus the Valid Inequality of minimum start-up and trip-out time of one unit, which is theoretically most "tight", is obtained; finally, the correctness of the most "tight" Valid Inequality is verified by simulation results of IEEE RTS 96 system and calculation of actual example.